Will artificial super-intelligence evolve to have selfishness inherent in biological systems?
AI will only "evolve" selfishness if it "evolves" in a competitive environment and has certain human-like faculties.

Self-protecting desires on the other hand are logical consequences of having any goal at all. After all, you can't reach your goal if you are destroyed. 

The concern of "evil" super intelligences isn't that they literally turn evil and selfish and cruel. Those are human qualities.

Instead a superintelligence that has a certain goal, will logically pursue subgoals that help it to reach the ultimate goal. Such subgoals will be resources, power, safety. 

So it will amass power and resources to reach its goal and exterminate any threat to its existence as long as its goal hasn't been reached, without being selfish at all.